The manager of a fast-food restaurant records each day for a year the amount of money received from sales of food that day. Using software, he finds a bell-shaped histogram with a mean of $1181 and a standard deviation of $201. Today the sales equaled $2041. Is this an unusually good day? Answer by providing statistical justification. Determine whether the total sales amount is unusual. Choose the correct answer below. A. No, this value is not unusual. A z-score outside of the range from −3 to 3 is not unusual. B. No, this value is not unusual. A z-score between −3 and 3 is not unusual. C. Yes, this value is unusual. A z-score between −3 and 3 is unusual. D. Yes, this value is unusual. A z-score outside of the range from −3 to 3 is unusual.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Given that,
The manager of a fast-food restaurant records each day for a year the amount of money received from sales of food that day.
Mean, = 1181
Standard deviation, = 201
Raw score, X = 2041
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